The prior-posterior-ratio (PPR) at \(\hat{p}_{1} \in [0, 1]\)  is given by \(R^{t}(\hat{p}_{1}) = \frac{\pi ^{0}(\hat{p}_{1})}{\pi ^{t}(\hat{p}_{1})}\) . Making use of the fact that the PPR evaluated at the true parameter value, \(p_{1}\) , is a martingale, it can be shown that the sequence of sets \((C^{t})_{t = 0}^{\infty }\) , where \(C^{t} \operatornamewithlimits{\stackrel{\text{\tiny def}}{=}}\lbrace \hat{p}_{1}: R^{t}(\hat{p}_{1}) < \frac{1}{\delta }\rbrace \) , is a \((1 - \delta )\) -confidence sequence for \(p_{1}\)  [1]}. In other words, we have the “anytime” guarantee that
\(\mathbb {P}\lbrace \: \exists \: t \ge 0: p_{1} \notin C^{t} \rbrace  \le \delta .\) 
